Displacive modulation

The structural parameters characterizing the modulated structure correspond to the average positions of the atoms, x, in the average unit cell as well as the components of the cosine and sine vector terms Cj and Sy . Clearly, the structure factor is similar to that of a conventional crystal structure but with an atomic contribution weighted by the rather cumbersome function g (h) containing the information about the modulation displacements. 

Hollow-fiber designs are being displaced by spiral-wound modules, which are inherently more fouling resistant, and require less feed pretreatment. Also, thin-film interfacial composite membranes, the best reverse osmosis membranes available, have not been fabricated in the form of hoUow-fine fibers. 

For ultrafiltration appHcations, hollow-fine fibers have never been seriously considered because of their susceptibiUty to fouling. If the feed solution is extremely fouling, tubular or plate-and-frame systems ate still used. Recentiy, however, spiral-wound modules with improved resistance to fouling have been developed, and these modules are increasingly displacing the more expensive plate-and-frame and tubular systems. Capillary systems are also used in some ultrafiltration appHcations. 

Air Backflush A configuration unique to microfiltration feeds the process stream on the shell side of a capillaiw module with the permeate exiting the tube side. The device is rim as an intermittent deadend filter. Eveiw few minutes, the permeate side is pressurized with air. First displacing the liquid permeate, a blast of air pushed back-... 

The two terms correspond to different polarization of phonons. The cosine term corresponds to displacements along the rotation axis or the direction tp = 0. The sine contribution arises from the phonons polarized along the line tp = The interaction (6.29) does not change the symmetry of the (p potential, and, in this respect, it is symmetric coupling, as defined in sections 2.3 and 2.5. Nonetheless, the role of the cosine and sine couplings is different. The former ( breathing modes ) just modulate the barrier (6.22), while the latter ( shaking modes ) displace the potential. 

AFM through force or displacement modulation techniques. Numerous methods have evolved that take advantage of the greater sensitivity modulation techniques provide, allowing dissipative processes to be examined. However, evaluation of the probe/sample response requires care with test protocols and instrument calibration, as well as application of appropriate contact mechanics models only a few of these techniques have evolved into quantitative methods. 

Asif, S.A.S., Wahl, K.J. and Colton, R.J., Nanoindentation and contact stiffness measurement using force modulation with a capacitive load-displacement transducer. Rev. Sci. Instrum., 70, 2408-2413 (1999). 

Equations (33) and (34) demonstrate that the motion quantities 5 (displacement) and v (velocity) are encoded in phase and frequency modulation of the detector output signal, purely referenced to the laser wavelength A. Tobeableto recover the time histories s(t) and v t) from the modulated detector signal, adequate phase and frequency demodulation techniques, or both, are utilized in the signal decoder blocks of a laser vibrometer. 

The observed NMR signal, S(k, q), is modulated by the two wave vectors the first, k, is related to the spatial density of the spins and the second, q, is related to a spatial displacement of spins ... 

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